The clean lines of 20th-century Sweden permeate Stockholm. Stroll down most any street of this affluent capital and you can feel the modernity and the tranquility. Yet Stockholm is a very old city, capital of a once warring and strongly monarchistic nation.

An easy walking tour in the heart of this city of islands lets you discover a bit of its history and, in the bargain, catch a glimpse of some of Sweden's greatest royal treasures. At the same time, you can enjoy the perquisites of the contemporary city. In fact, you can start in the present and work backward.

Take the city's predictably efficient subway to Gamla Stan -- literally the "old city." Gamla Stan sits at the meeting point of Lake Ma laren and the Baltic Sea. Established in the mid-13th century as a stronghold against Finnish invasion, this was the first of Stockholm's 14 islands to be settled and for centuries was the only one with much population or commerce: The territory beyond this half-mile-square rock was considered unfriendly hinterland by early Stockholmers. In fact, the city derives its name from this xenophobia. Long poles, or stocks, were driven into the waters around Gamla Stan to keep invaders and most others from landing their ships on the holme, or island.

By the mid-17th century, crowding, pollution and disease were so widespread on Gamla Stan that the city began serious movement outward. Today you can go to and from Gamla Stan without really being aware of crossing what were once major water barriers. This is especially true when arriving on the green cars of the Stockholm metro.

Exiting the Gamla Stan station and crossing into the heart of the old city is a walk back in time. Instead of the broad and straight traffic-clogged boulevards of the rest of the city, narrow curving lanes -- many too small for vehicles -- beckon. In place of tall glass and steel or stone buildings are three- and four-story stucco structures. The old quarter bustles in the late afternoon, as Gamla Staners scurry back to their ancient, and expensive, flats (a pied-a`-terre in Gamla Stan is the dream of most Stockholmers) and shoppers seek out the many boutiques.

Any of several lanes leads to the heart of Gamla Stan. Yxsmedsgrand, for example, takes you to Stora Nygatan, the quarter's main traffic street. Barely large enough for cars to pass but wide by Gamla Stan measures, Stora Nygatan is crowded with shops, appealing patisseries and tea rooms: The elegantly appointed Alexanders The o Kaffehadel is a full-service coffee and tea shop, the windows of Walles Musid feature a sparkling display of brass instruments.

From Stora Nygatan walk up the curving Goran Halsinges Grandeto Vasterlanggatan. This unusual pedestrians-only street offers everything from hole-in-the-wall ice cream and sandwich windows (such as Korv Mos at No. 59) to svelt objets d'art salons like Latona Antik next door. In the basement of the Spabanken at No. 48 you can see a section of the original city wall. Cafe Art at No. 62 is a charming spot, seemingly cut into this wall. An underground series of rooms connected by low brick arches, with modern paintings on the walls and classical music in the background, Cafe Art is reached by going past a set of iron gates into a small courtyard, then descending down 19 stone steps. It makes an excellent refreshment and people-watching stop.

Just to the east is a series of little streets lined by particularly attractive houses, all of which sport distinctive decorations that seem to resemble branding-iron ends. These dark metal mosaics with their seemingly endless designs -- curves, squiggles, squares, ovals -- are, in fact, quite functional, serving as end pieces for floor bracing.

Gamla Stan has little open space other than its streets. But periodically you will see a widening, with a fountain in the middle; these were carriage turnarounds in preautomobile days. One of the larger open spaces, albeit still quite small, is found just off Vasterlanggatan. This is the courtyard of the 17th-century German Church, known for its gilded altar. The church courtyard affords an enchanting place to rest, especially in late afternoon as vesper bells play.

The labyrinth of Gamla Stan streets and lanes can provide hours of entertainment for the pedestrian traveler. Meandering through this labyrinth toward the Storkyrkan (Cathedral) and the Royal Palace (on the northern end of the island) will eventually lead you to the Stortorg, the original square of Gamla Stan. A cobblestoned expanse less than 100 yards across, the Stortorg presents an array of subtly colored fac ades of high, narrow 17th- and 18th-century buildings. It was here that fishermen gathered daily, for centuries, to meet, talk and sell their catches. Today the Stortorg is a highly sought-after residential area.

From the Stortorg it is a short walk to the Stockholm Cathedral and the formidable Royal Palace. The Cathedral, which dates from 1306 but was remodeled in the baroque style in the 18th century, personifies Swedish society of today -- solid, quiet, with a bit of flourish. The Cathedral's frequent noontime organ concerts offer one of the best times for exploring its odd mix of staid and fanciful architecture and appointments.

The Royal Palace is the seat of what many Swedes sardonically refer to as their "socialist monarchy." While possessing only ceremonial power, King Carl XVI Gustaf and Queen Silvia have a symbolic prominence in Sweden akin to that of their 609-room palace. (The royal residence is actually Drottningholm Palace, but the royal offices are at the Royal Palace, and official functions also are held there.)

The Changing of the Guard at noon (1 p.m. on Sundays) in the large interior palace courtyard renders a bit of living history, but two museums in the cavernous palace basement provide considerably more historical color: the Royal Armoury and the Treasury.

The Royal Armoury houses a stunning exhibit of royal wardrobes and coaches, in addition to some handsome suits of armor. It was started in 1627 when King Gustavus II Adolphus sent back his bloodied uniform from a battle in Poland to serve as a reminder to his people of the grim side of war. That tattered garb can be seen today in the Armoury, as can the clothes in which he was killed five years later in a Thirty Years War battle at Lu tzen and the stuffed white mount he was riding when he fell.

There are more than 900 other garments in the Armoury, many of which are grouped in a collection called "Royal Fashion," opened last spring. Included are the wedding suit of Gustavus Adolphus and the all-gold-thread coronation gown of Charles II, which was saved from a fire in 1697 by being thrown out of a palace window.

The Royal Armoury also has a spectacular collection of royal coaches, including the large coronation coach made in the 1690s for Karl XII. This exquisitely fashioned gilded coach is more than 25 feet long and 12 feet high, with a colorful crown perched on top.

If the contents of the Royal Armoury don't dazzle you, those in the Treasury will. It is here that Sweden's crown jewels are shown in an intimate setting. In illuminated small glass cases in darkened chambers, the crown scepters, orbs, swords and keys sitting on velvet cushions are as impressive in their workmanship as in the sheer dollar value of the gold, silver and gems of which they are made.

Two ceremonial swords from the 15th- and 16th-century reign of Gustavus Vasa, each a meter long, start the collection. These gold-plated sabers bear intricately etched scenes from the Old Testament. A dozen breathtaking crowns from past kings and queens (Sweden stopped coronations after Oskar II in 1872) fill the small rooms of the Treasury. The most treasured of these treasures is Erik XIV's ruby-, emerald- and pearl-adorned crown, made from Flemish gold in 1561. (Some of the pieces from the Treasury, as well as the Armoury, will be coming to the United States this spring as part of the New Sweden 350th anniversary of the first Swedish settlement in this country. The exhibition will be at the National Gallery from April 13 to Sept. 5.)

The transition from the dark and bejewelled vaults of the Treasury back onto the bright esplanade in front of the palace is a striking one, as you emerge from centuries-old royal Stockholm into the present. Just to the north of the palace, on a tiny adjacent island, is Parliament, with its very modern and airy chamber, framed by a 500-square-foot contemporary tapestry in 200 shades of gray. The contrast of Parliament with the Royal Palace speaks for the contrast of the old and new Stockholm that unfolds before visitors to this handsome Scandinavian capital.

Arthur H. Purcell is a Washington-based policy analyst whose work takes him around the country.

GETTING THERE: TWA, Lufthansa and Northwest are among the international airlines that provide connecting service from Washington to Stockholm, via New York. The least expensive APEX fare -- offered by both TWA and Northwest -- is currently $588 round trip; tickets must be purchased 30 days in advance, and travel is restricted to certain days of the week.

GETTING AROUND: Taxis are expensive in Stockholm, and not always easy to find. But the bus and subway system is efficient and fairly inexpensive, and there are one-, two- and three-day Tourist Cards available -- for approximately $10 a day -- that allow unlimited transportation. With a fare-card system similar to Washington's Metro, the Stockholm subway, called Tunnelbana, fans out in all directions of the city and its suburbs. The stations are marked with a large blue "T."

WHERE TO STAY: Hotels in Stockholm tend to be solid and comfortable, with rates ranging upward from $90 double. The Diplomat is typical of their quality, with well-appointed rooms that feature French-door-sized windows facing a boat harbor in front and an old church in back. Guests go to their rooms by either a winding marble staircase or an ancient elevator in a cage. Across the water, nearer Gamla Stan, is the elegant Strand Hotel, featuring the upscale Piazza dining room. The Piazza is a roofed courtyard designed to resemble a stereotypic urban Italian setting, with lines of carefully placed laundry hanging above the diners.

WHERE TO EAT: Stockholm abounds in good food and drink, and Gamla Stan is no exception. For example, Fem Sma Hus, at Nygrand 10, is an elegant restaurant of nine intimate rooms in the basement of five small houses that have long been joined together. At Fem Sma Hus you can dine on top-quality seafood (pike is a specialty) under your own private brick arch in a candlelight setting. For simpler fare try the Old Town Cafe' near the Cathedral.

INFORMATION: Scandinavian Tourist Information Office, 655 Third Ave., New York, N.Y. 10017, (212) 949-2333.